Split vanilla beans lengthwise with a sharp paring knife. Gently scrape out all the seeds.
Place vanilla-bean scrapings and pods in a medium saucepan with milk. Scald the mixture, cover, and remove from heat. Let steep for 30 minutes.
Combine egg yolks and sugar in the bowl of an electric mixer fitted with the whisk attachment. Beat at medium-high speed until very thick and pale yellow, 3 to 5 minutes. Alternatively, whisk together in a medium bowl.
Return milk to stove, and bring just to a simmer. Using a measuring cup or ladle, slowly pour about 1/2 cup of the hot-milk mixture into the egg-yolk mixture, whisking constantly on low speed until blended. Keep adding milk mixture, about 1/2 cup at a time, until it has all been added. Whisk until combined.
Pour mixture back into saucepan, and cook over low heat, stirring constantly with a wooden spoon, until mixture is thick enough to coat the back of a spoon, 3 to 5 minutes. The custard should retain a line drawn across the back of the spoon with your finger.
Fill a large bowl with ice and water. Remove pan from heat, and immediately stir in chilled cream to stop the custard from cooking. Pour through a mesh sieve into a medium bowl set in the ice bath, and stir occasionally until cooled. (Discard vanilla-bean pod and strained seeds.) Stir vanilla extract into cooled custard. Cover bowl, and transfer to refrigerator until chilled, at least 30 minutes or overnight.
Pour custard into an ice-cream maker, following the manufacturer's instructions. Churn until the ice cream is just set, but not hard.
Transfer soft ice cream to an airtight plastic container; freeze at least 4 hours and up to 1 week.